Password Entropy Explained: How It's Actually Calculated

Every password strength meter — including the one on our password generator — reports a number in bits: “71 bits,” “104 bits.” That number is entropy, and it isn’t a vibe or a marketing score. It comes from one formula, applied consistently, and once you know the formula you can predict exactly how any change to length or character set moves the number.

The formula

Password entropy in bits is:

entropy = length × log2(charset size)

Each character drawn independently and uniformly at random from a charset of size k contributes log2(k) bits, because log2(k) is exactly the number of yes/no questions needed on average to pin down one character out of k possibilities. String together n such characters and the bits simply add, giving n × log2(k). This is the same definition of entropy used across information theory, not a password-specific invention.

Worked examples

Here’s the formula applied to the character sets a typical generator offers:

Two patterns fall out of this table. First, length dominates: going from 12 to 16 characters on the full charset adds 26 bits, while adding symbols to a 12-character alphanumeric password only adds about 8 bits. Second, the marginal value of a bigger charset shrinks — going from 62 to 94 possible characters buys 0.6 more bits per character, far less than the 1.25-bit jump from adding uppercase to lowercase-only. This is exactly why length-first advice, including our own guidance on picking a strong password, is the current consensus rather than complexity rules.

What entropy does and doesn’t measure

The formula assumes every character is drawn independently and uniformly at random — which is true for a generator using a cryptographic random source, and false for almost every password a human types from memory. Humans lean on dictionary words, keyboard patterns, and predictable substitutions, all of which an attacker’s cracking dictionary already accounts for. A password that “looks” high-entropy by naive character counting — say, P@ssw0rd123!— is trivially guessed in practice, because it isn’t actually a random draw from the full charset; it’s a well-known pattern with a few substitutions layered on. Entropy math only applies cleanly to passwords that are genuinely random, which is the whole argument for generating rather than composing them.

How much entropy is enough

NIST SP 800-63B , the federal digital-identity standard, doesn’t prescribe a bit target directly — it instead sets a minimum length (8 characters for user-chosen secrets, longer strongly encouraged) and pushes verifiers to screen against known- breached password lists rather than force arbitrary complexity rules. In practice, security teams commonly treat roughly 80 bits as the threshold where offline brute-force becomes infeasible for the foreseeable future, and 100+ bits as comfortably future-proof. Looking at the table above, that means 14+ random alphanumeric-plus-symbol characters, or a random 16-character password on any reasonable charset.